Homology of the double and the triple loop spaces¶of E6, E7, and E8

We study the mod p homology of the double and the triple loop spaces of exceptional Lie groups E ₆, E ₇, and E ₈ through the Eilenberg–Moore spectral sequence and the Serre spectral sequence using homology operations. The Bockstein actions on them are also determined. As a result, the Eilenberg–Moore spectral sequences of the path loop fibrations converging to H _*(Ω² G;? _p ) and H _*(Ω³ G;? _p ) collapse at the E ²-term for any compact simple Lie group G. Received: 11 November 1999     

Soret effects on the onset of convection in rotating porous layers via the “auxiliary system method”

The onset of convection in a ternary horizontal porous fluid layer, heated from below and salted from above and below, in the presence of Soret thermo-diffusive effects (in the Darcy–Boussinesq scheme) is investigated. Via a new approach (“auxiliary system method”), it is shown that do not exist subcritical instabilities and that the global nonlinear stability is guaranteed by the linear stability. The Soret stabilizing-destabilizing effects, via algebraic conditions in closed forms, are obtained also discovering symmetries and skew-symmetries hidden in the Darcy–Boussinesq equations.     

Initial layers and zero-relaxation limits of Euler–Maxwell equations

In this paper we consider zero-relaxation limits for periodic smooth solutions of Euler–Maxwell systems. For well-prepared initial data, we propose an approximate solution based on a new asymptotic expansion up to any order. For ill-prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in time intervals independent of the relaxation time and their convergence is justified by establishing uniform energy estimates.     

On Existence of the Maximum Solution and Estmates on Moments of Absolutes Maximum of the Solution for Poisson S．D．E in the Plane

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On the Extension of Isometries between Unit Spheres of E and C（Ω）

In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too.     

Iterated souslin forcing,the principles ⋄(E) and a generalisation of the axiom SAD

The axiom SAD was introduced in our paper with Avraham and Shelah [1]. It is a Martin’s Axiom type of principle, having some of the consequences of MA plus , but nonetheless provably consistent with GCH. In [1] it was shown to be consistent (with GCH) and used to demonstrate the consistency with CH of some known consequences of MA + . In particular, SAD implies the negation of Jensen’s ⋄ principle. In this paper we present a generalisation of SAD, let us call it SAD(E), whereE will be an arbitrary stationary subset ofω ₁, and show that although SAD(E) implies the negation of ⋄(E), it is consistent with ⋄. SAD(E) resembles the axiom SA of Shelah, described in our survey article [2], and indeed is a sort of blending of the two principles SA and SAD. (In particular, Shelah proved that SA is consistent with ⋄ but implies the failure of some ⋄(E).) Our proof (of the consistency of SAD(E) with ⋄) will be of interest to forcing enthusiasts, since it shows that iterated Souslin forcingcan distinguish between different stationary sets (it was previously thought that this was not the case), and can indeed be used to establish the non-provability of the principles ⋄(E) from ⋄ alone.     

A tale of mathematical myth-making: E T Bell and the ‘arithmetization of algebra’

Throughout E T Bell’s writings on mathematics, both those aimed at other mathematicians and those for a popular audience, we find him endeavouring to promote abstract algebra generally, and the postulational method in particular. Bell evidently felt that the adoption of the latter approach to algebra (a process that he termed the ‘arithmetization of algebra’) would lend the subject something akin to the level of rigour that analysis had achieved in the nineteenth century. However, despite promoting this point of view, it is not so much in evidence in Bell’s own mathematical work. I offer an explanation for this apparent contradiction in terms of Bell’s infamous penchant for mathematical ‘myth-making’.     

Extension of Isometries Between the Unit Spheres of Normed Space E and C（Ω）

In this paper, we study the extension of isometries between the unit spheres of normed space E and C（Ω）. We obtain that any surjective isometry between the unit spheres of normed space E and C（Ω） can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley＇s problem （where Ω be a compact metric space）.     

Interior penalty discontinuous approximations of convection–diffusion problems with parabolic layers

Summary A nonsymmetric discontinuous Galerkin finite element method with interior penalties is considered for two–dimensional convection–diffusion problems with regular and parabolic layers. On an anisotropic Shishkin–type mesh with bilinear elements we prove error estimates (uniformly in the perturbation parameter) in an integral norm associated with this method. On different types of interelement edges we derive the values of discontinuity–penalization parameters. Numerical experiments complement the theoretical results.     

The K°-relation on the Congruence Lattice of a Regular Semigroup with an Inverse Transversal

Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation K° on C(S) is introduced as follows: if ρ, θ∈ C(S), then we say that ρ and θ are K°-related if Ker ρ° = Ker θ° , where ρ° = ρ|S°. Expressions for the least and the greatest congruences in the same K°-class as ρ are provided. A number of equivalent conditions for K° being a congruence are given.